Letter of T>r Wallis/^? T)r Sloan^ concern- 
ing the Quadrature of the Parts of the 
Lunula of Hippocrates Ghius ^ performed 
jVfrJohn Perks; with the further Im- 
provements of the fame ^ hy Dr David 
Gregory , and iV/r John Cafwell. 
SIR, 
TH E S<^uartng a certain Lunuh by Hippocrates Chius 
long lince, hath been known (as to the whole Lumla) 
for many Ages. But (as to the Tarts of it, and the Ap- 
purtenances thereunto,) New Difcoveries have been lately made, 
which (I think) had not been confider'd by any before this pre- 
lent Age. 
I received (in November i(5pp.) from Mr. John Terks (Mailer 
of an Hofpital at Old-Svoynford in WorcefteY-Jhtre^ founded by 
Mr, Thomas Foley) a brief account of his S^uariug the Tortions of 
Hippocrates^ Lumda ; with which ( I prefume ) you will not be 
difpleafed. 
For the better underftanding of which ; I (hall premife as 
known ( becaule long Cnce demonftrated, ) That, If on A B (the 
Chord of ADB, the Quadrantal Arc of a Greater Circle, who's 
Center is C, ) be defcribed, as on a Diameter, a Semi-circle ABE ; 
Rrr This 
